Pierre Van MOERBEKE
(Louvain University and Clay Mathematical Institute)

Random permutations and matrices, and integrable systems

This mini-course will cover the following subjects:
  1. Longest increasing sequences in random permutations and words
  2. The spectrum of random matrices
  3. Large random permutations and large random matrices: asymptotics

Slides of the Course:

Further References:

  1. P. van Moerbeke, ``Integrable lattices: random matrices and random permutations'', in Random matrices and their applications, Mathematical Sciences research Institute Publications Vol. 40, Cambridge University Press, pp. 321-406, (2001).
  2. M. Adler and P. van Moerbeke, ``Hermitian, symmetric and symplectic random ensembles: PDE's for the distribution of the spectrum'', Annals of Mathematics, 153 (2001) 149-189; math-ph/0009001.
  3. A. Borodin, A. Okounkov and G. Olshanski, ``Asymptotics of Plancherel measures for symmetric groups'', J. Amer. Math. Soc. 13 (2000) 481--515; math.CO/9905032.
  4. C.A. Tracy and H. Widom, ``Level-Spacings distribution and the Airy kernel'', Comm. Math. Phys., 159 (1994) 151-174; hep-th/9211141.
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